Sliced symmetrical Latin hypercube designs

A main goal in computer experiments is to estimate the expected model output. This article proposes a new type of space-filling design, called a sliced symmetrical Latin hypercube, intended for solving this integration problem when multiple computer models are run in batches. Such a design is a special Latin hypercube that can be partitioned into slices of smaller Latin hypercubes, with some slices being also symmetrical designs. Compared with an ordinary sliced Latin Hypercube, the proposed design has the following advantages: (i) the group symmetry of models can be detected by the first slice of the design, which leads to a decline in the experimental cost, (ii) the design structure inherits efficient variance reduction ability for the estimation from the sliced Latin Hypercubes, and (iii) each slice of the design is flexible in run size. Finally, numerical illustrations are provided to corroborate the theoretical results.